Reducing the Computational Time for the Kemeny Method by Exploiting Condorcet Properties

Rico, Noelia; Vela, Camino R.; Pérez‐Fernández, Raúl; Dı́az, Irene

doi:10.3390/math9121380

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…In the last years, Azzini and Munda [7] introduced an exact algorithm that greatly improved the runtime in relation to others published before [8,9]. We have improved these results in [10,11], ensuring the feasibility of the execution up to 13 alternatives. However, the runtime of the branch and bound algorithms (B &B) proposed in these works depends on the characteristics of the input profiles and cannot be exactly known prior to the execution.…”

Section: Introductionmentioning

confidence: 80%

Kemeny ranking aggregation meets the GPU

2023

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Ranking aggregation, studied in the field of social choice theory, focuses on the combination of information with the aim of determining a winning ranking among some alternatives when the preferences of the voters are expressed by ordering the possible alternatives from most to least preferred. One of the most famous ranking aggregation methods can be traced back to 1959, when Kemeny introduces a measure of distance between a ranking and the opinion of the voters gathered in a profile of rankings. Using this, he proposed to elect as winning ranking of the election the one that minimizes the distance to the profile. This is factorial on the number of alternatives, posing a handicap in the runtime of the algorithms developed to find the winning ranking, which prevents its use in real problems where the number of alternatives is large. In this work we introduce the first algorithm for the Kemeny problem designed to be executed in a Graphical Processing Unit. The threads identifiers are codified to be associated with rankings by means of the factorial number system, a radix numeral system that is then used to uniquely pair a ranking with the thread using Lehmer’s code. Results guarantee constant execution time up to 14 alternatives.

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Section: Introductionmentioning

confidence: 80%

Kemeny ranking aggregation meets the GPU

2023

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“…This process was repeated 50 times, obtaining 50 different rankings, then aggregated using scoring ranking rules and assigning each candidate with a score, finally obtaining variable importance. Although many different ways may obtain a consensus ranking (28,29,30,31,32), the Borda count is a quite simple convex-ranking-rule (8), already successfully applied similarly by Rúa et al (2023).…”

Section: Analysis Of Relevant Featuresmentioning

confidence: 99%

About identification of features that affect the estimation of citrus harvest

Bóbeda¹,

Mazza²,

Rico³

et al. 2023

Rev. FCA UNCUYO

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Accurate models for early harvest estimation in citrus production generally involve expensive variables. The goal of this research work was to develop a model to provide early and accurate estimations of harvest using low-cost features. Given the original data may derive from tree measurements, meteorological stations, or satellites, they have varied costs. The studied orchards included tangerines (Citrus reticulata x C. sinensis) and sweet oranges (C. sinensis) located in northeastern Argentina. Machine learning methods combined with different datasets were tested to obtain the most accurate harvest estimation. The final model is based on support vector machines with low-cost variables like species, age, irrigation, red and near-infrared reflectance in February and December, NDVI in December, rain during ripening, and humidity during fruit growth. Highlights: Red and near-infrared reflectance in February and December are helpful values to predict orange harvest. SVM is an efficient method to predict harvest. A ranking method to A ranking-based method has been developed to identify the variables that best predict orange production.

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“…Borda is a positional voting procedure where each voter provides a ranking in the group decision problem [14,77,81,82]. An individual preference profile is expressed in terms of an ordinal ranking over the available alternatives to choose from [23].…”

Section: Borda Voting Proceduresmentioning

confidence: 99%

“…Condorcet (1743-1794) postulated his own model based on philosophical arguments; he was Borda's main antagonist. According to his model, the winning candidate is the one who defeats the rest of the candidates by a simple majority in pairwise comparisons, which implies that there will not always be a winner [58,73,82,83,89].…”

Section: Condorcet's Ranking Voting Proceduresmentioning

confidence: 99%

The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures

García-del-Valle-y-Durán

Hernández‐Martínez

Fernández‐Anaya

2022

Mathematics

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Consensus or conflict agreements, and how these change over time, have significant consequences for understanding the network behavior of human beings, especially when it is necessary to have agreements to move companies and countries forward peacefully. This paper proposes a new Greatest Common Decision Maker (GCDM) aggregation voting procedure applied to square preference matrices of n alternatives and n decision makers. An analysis of the mathematical combinatory ranking of consensus and conflicts generated by the GCDM is realized, and compared to the well-known Borda, Pluralism and Condorcet aggregation procedures to cover the entire class of dynamic accountable group decision-making phenomena. A classification for the family of magic squares is reviewed and it is determined that a conflict decision matrix corresponds to a Latin square. As an original contribution, a 2D color heatmap is generated as a visual tool to compare the consensus and conflict cases generated by the compared methods. Finally, a new consensus reaching model is proposed to compare these aggregation methods defining cost and effort change matrices to convert the cases of conflicts into consensus according to the change in individual preferences. The incorporation of social concepts into our research makes the results obtained stronger.

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Reducing the Computational Time for the Kemeny Method by Exploiting Condorcet Properties

Cited by 6 publications

References 14 publications

Kemeny ranking aggregation meets the GPU

Kemeny ranking aggregation meets the GPU

About identification of features that affect the estimation of citrus harvest

The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures

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